Abstract: Investigating clinical hypotheses of diseases and their potential therapeutic implications based on large medical image collections is an important research area in medical imaging. Medical images provide insights about anatomical changes caused by diseases without harmful side effects; hence is critical to disease diagnosis and treatment planning. However, the characterization and quantification of such anatomical changes pose computational and statistical challenges due to the high-dimensional and nonlinear nature of the data. In this talk, I will introduce efficient, robust, and reliable methods to address these problems. My approach entails developing a low-dimensional shape descriptor to represent anatomical changes in large-scale image data sets, and novel Bayesian machine learning methods for analyzing the intrinsic variability of high-dimensional manifold-valued data with automatic dimensionality reduction and parameter estimation. The potential practical applications of this work beyond medical imaging include machine learning, computer vision, and computer graphics.